Inverse Optimal Control for Passive Network Systems

Passivity-based approaches have been suggested as a solution to the problem of decentralized control design in many multi-agent network control problems as stability can often be determined independently of the network topology. However, it is not clear if these controllers are optimal at a network level due to their inherently local formulation, with designers often relying on heuristics to achieve desired global performance. On the other hand, solving for an optimal controller is not guaranteed to produce a decentralized optimal policy that leads to a passive network with a plug-and-play operation. In this paper we address these dual problems by showing that when appropriate decentralized conditions are satisfied, passive network systems have an inverse optimal control interpretation, i.e. the corresponding decentralized controllers are solutions to a network-wide optimal control problem. These conditions are then formulated into a set of linear matrix inequalities (LMIs) for the case of linear systems, which can be used for control synthesis for such systems. The proposed approach is demonstrated through case studies from distributed optimization and the control of DC microgrids.